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geometry

Color photo of Jordan Ellenberg sitting with a laptop by a lake at sunset
Q&A

A Number Theorist Who Connects Math to Other Creative Pursuits

By Steve Nadis
May 27, 2021
Read Later

Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.

Illustration of figures building a large structure, with a new material being used for the latest additions
polynomials

Mathematicians Find Long-Sought Building Blocks for Special Polynomials

By Kelsey Houston-Edwards
May 25, 2021
Read Later

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.

topology

How Mathematicians Use Homology to Make Sense of Topology

By Kelsey Houston-Edwards
May 11, 2021
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Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.

Quantized Academy

How to Solve Equations That Are Stubborn as a Goat

By Patrick Honner
May 6, 2021
Read Later

Math teachers have stymied students for hundreds of years by sticking goats in strangely shaped fields. Learn why one grazing goat problem has stumped mathematicians for more than a century.

geometry

Statistics Postdoc Tames Decades-Old Geometry Problem

By Erica Klarreich
March 1, 2021
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To the surprise of experts in the field, a postdoctoral statistician has solved one of the most important problems in high-dimensional convex geometry.

An illustration of a doughnut-shaped elliptic curve intertwined with the Julia set.
number theory

Mathematicians Set Numbers in Motion to Unlock Their Secrets

By Kelsey Houston-Edwards
February 22, 2021
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A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.

Abstractions blog

Undergraduates Hunt for Special Tetrahedra That Fit Together

By Kevin Hartnett
February 9, 2021
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A group of MIT undergraduates is searching for tetrahedra that tile space, the latest effort in a millennia-long inquiry. They’ve already made a new discovery.

Colorful isualization of the 59 isolated examples of tetrahedra that have rational dihedral angles
geometry

Tetrahedron Solutions Finally Proved Decades After Computer Search

By Kevin Hartnett
February 2, 2021
Read Later

Four mathematicians have cataloged all the tetrahedra with rational angles, resolving a question about basic geometric shapes using techniques from number theory.

Illustration of mathematicians descending through a cavern whose walls are lined with polynomials.
polynomials

Mathematicians Resurrect Hilbert’s 13th Problem

By Stephen Ornes
January 14, 2021
Read Later

Long considered solved, David Hilbert’s question about seventh-degree polynomials is leading researchers to a new web of mathematical connections.


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